Properties

Level $31$
Weight $0$
Character 31.1
Symmetry odd
Fricke sign $-1$

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Maass form invariants

Level: \( 31 \)
Weight: \( 0 \)
Character: 31.1
Symmetry: odd
Fricke sign: $-1$
Spectral parameter: \( 3.37678368162 \)

Maass form coefficients

\(a_{1}=+1.000000000\) \(a_{2}=+1.520161321\) \(a_{3}=+0.155325021\) \(a_{4}=+1.310890442\) \(a_{5}=+1.587565835\)
\(a_{6}=+0.236119089\) \(a_{7}=+0.306637753\) \(a_{8}=+0.472603624\) \(a_{9}=-0.975874138\) \(a_{10}=+2.413356177\)
\(a_{11}=+0.123874197\) \(a_{12}=+0.203614085\) \(a_{13}=-0.735214097\) \(a_{14}=+0.466138852\) \(a_{15}=+0.246588697\)
\(a_{16}=-0.592456692\) \(a_{17}=+0.333011451\) \(a_{18}=-1.483486118\) \(a_{19}=-1.720479994\) \(a_{20}=+2.081124879\)
\(a_{21}=+0.047628516\) \(a_{22}=+0.188308763\) \(a_{23}=+1.304558336\) \(a_{24}=+0.073407168\) \(a_{25}=+1.520365281\)
\(a_{26}=-1.117644034\) \(a_{27}=-0.306902692\) \(a_{28}=+0.401968500\) \(a_{29}=+0.751349302\) \(a_{30}=+0.374854599\)
\(a_{31}=+0.179605302\) \(a_{32}=-1.373233371\) \(a_{33}=+0.019240762\) \(a_{34}=+0.506231127\) \(a_{35}=+0.486807621\)
\(a_{36}=-1.279264079\) \(a_{37}=-1.386159082\) \(a_{38}=-2.615407140\) \(a_{39}=-0.114197145\) \(a_{40}=+0.750289368\)
\(a_{41}=+0.897077245\) \(a_{42}=+0.072403027\) \(a_{43}=+0.742685781\) \(a_{44}=+0.162385501\) \(a_{45}=-1.549264441\)
\(a_{46}=+1.983139123\) \(a_{47}=+0.011105005\) \(a_{48}=-0.092023348\) \(a_{49}=-0.905973288\) \(a_{50}=+2.311200494\)
\(a_{51}=+0.051725011\) \(a_{52}=-0.963785133\) \(a_{53}=+1.660804292\) \(a_{54}=-0.466541602\) \(a_{55}=+0.196658443\)
\(a_{56}=+0.144918114\) \(a_{57}=-0.267233591\) \(a_{58}=+1.142172148\) \(a_{59}=+0.631078981\) \(a_{60}=+0.323250766\)
\(a_{61}=-1.406811781\) \(a_{62}=+0.273029033\) \(a_{63}=-0.299239853\) \(a_{64}=-1.495079564\) \(a_{65}=-1.167200783\)
\(a_{66}=+0.029249063\) \(a_{67}=-0.237841303\) \(a_{68}=+0.436541528\) \(a_{69}=+0.202630551\) \(a_{70}=+0.740026117\)
\(a_{71}=+0.029438449\) \(a_{72}=-0.461201654\) \(a_{73}=+1.027036057\) \(a_{74}=-2.107185421\) \(a_{75}=+0.236150769\)
\(a_{76}=-2.255360779\) \(a_{77}=+0.037984506\) \(a_{78}=-0.173598083\) \(a_{79}=+0.572988538\) \(a_{80}=-0.940564003\)
\(a_{81}=+0.928204471\) \(a_{82}=+1.363702130\) \(a_{83}=+1.927736080\) \(a_{84}=+0.062435766\) \(a_{85}=+0.528677602\)
\(a_{86}=+1.129002198\) \(a_{87}=+0.116703346\) \(a_{88}=+0.058543395\) \(a_{89}=+0.053968411\) \(a_{90}=-2.355131878\)
\(a_{91}=-0.225444399\) \(a_{92}=+1.710133053\) \(a_{93}=+0.027897197\) \(a_{94}=+0.016881399\) \(a_{95}=-2.731375259\)
\(a_{96}=-0.213297502\) \(a_{97}=+0.015615830\) \(a_{98}=-1.377225550\) \(a_{99}=-0.120885625\) \(a_{100}=+1.993032314\)

Showing 100 of 546 available coefficients

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